The sport fishery in Seward, Alaska

An investigation into the spatial distribution of use by charter fishermen and the size of sport-caught Pacific halibut in Seward, Alaska over the last two decades

Leslie Gains-Germain, Montana State University, M.S. Statistics Candidate

$fish$

"We travel farther for smaller fish"

Questions of Interest

Data from Alaska Department of Fish and Game

Question 1: Is there evidence that the distance Seward charter boats travel to fish for bottomfish has changed over the years 1993-2014?

Logbook Data

Interview Data

Question 2: Is there evidence of a change in the mean length of halibut caught by Seward fishermen over the years 1994-2013?

Biological Data

Data Reference

ADF&G Saltwater Logbook Database. 2004-2013. Anchorage, AK: Alaska Department of Fish and Game, Divison of Sport Fish. Intranet. Accessed 15 Dec 2014. Custom query details available upon request from ADF\&G, Division of Sport Fish, Research and Technical Services.

ADF&G non-confidential data. 1993-2014. Homer, AK: Alaska Department of Fish and Game, Division of Sport Fish. Personal communication, Scott Meyer.

ADF&G non-confidential data. 1994-2013. Homer, AK: Alaska Department of Fish and Game, Division of Sport Fish. Personal communication, Scott Meyer.

Logbook Data 2004-2013

Logbook: 2004-2013

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Interview Data 1993-2014

Two days a week randomly selected for interviews
Effort spread across the four harbor cleaning stations
Each boat is asked:

Did you catch bottom fish today?
If yes, record trip type
Identify the primary statistical area where the majority of bottomfish were caught.

abbreviation	description
H	halibut exclusively
B	any combination of bottomfish (halibut, rockfish, lingcod, Pacific cod, sharks)
B+S	any combination of bottomfish and salmon (e.g. halibut+coho)

Interview 1993-2014

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Comparison- Cape Cleare

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Fitted Probabilities and 95% Pointwise CIs

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The odds of fishing in Cape Cleare in $2014$ are estimated to be $2.43$ times the odds of fishing in Cape Cleare in $1993$, with a $95\%$ confidence interval from $1.22$ to $4.92$ times.

The odds of NOT fishing in Resurrection Bay in $2014$ are estimated to be $2.78$ times the odds of NOT fishing in Resurrection Bay in $1993$, with a $95\%$ confidence interval from $1.32$ to $5.82$ times.

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Question 2: Is there evidence of a change in the mean length of halibut caught by Seward fishermen over the years 1994-2013?

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Biological Data 1993-2013

Three days a week randomly selected for biological sampling
Boats selected (non-random) and entire catch is studied

port	sector	date	age	length	sex	statarea	length.in	area
Seward	Charter	5261994	11	120.0	F	495938	47.24	resbay
Seward	Charter	5261994	NA	128.0	F	475934	50.39	capecleare
Seward	Charter	5261994	13	85.0	M	475934	33.46	capecleare
Seward	Charter	5261994	13	85.5	M	475934	33.66	capecleare
Seward	Charter	5271994	11	126.5	F	485935	49.80	junken
Seward	Charter	5271994	11	95.8	F	475934	37.72	capecleare

Average fish lengths plotted over time

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In the waters around Cape Junken, there is strong evidence of a relationship between mean fish length, on the log scale, and time over the years $1994$ to $2013$ (two-sided p-value$<0.0001$ from t-stat$=-5.520$ on $18$ df).

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The median halibut length in Cape Junken is estimated to have decreased by $16.5$% over the years $1994$ to $2013$, with a $95$% confidence interval from a $11.0$% to a $21.6$% decrease.

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95% CI for percentage change in median fish length 1994-2013 in Cape Cleare

OLS-black dashed line (-20.4%, 3.76%)

WLS-blue line (-22.4%, -5.34%)

Mixed Effects-red line (-19.7%, -0.43%)

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Scope of Inference

Technically does not extend to all Seward boats/fish, BUT....

No causal

Questions?

Comparison - Resurrection Bay

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Comparison - Patton Bay

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Quasibinomial Logistic Regression

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Each area modeled separately
Assumptions

Independence
Linearity
Outliers

Results

There is moderate evidence that the log odds of fishing at Cape Cleare changes over time, assuming a linear trend over years $1993$ to $2014$ (p-value$=0.02479$ from drop-in-deviance F-stat$=5.89$).

	YEAR coef	SE	F-stat	Pr(>F)
capecleare	0.0404	0.0161	5.891	0.0248
resbay	-0.0463	0.0171	7.351	0.0134
nuka	0.0188	0.0385	0.238	0.6309
patton	0.0760	0.0200	12.532	0.0021

Mixed Effects Model

Each area modeled separately

$length_{i}=\beta_0+\beta_1year_i+\alpha_{i}+\epsilon_{i}$

$\epsilon_{i} \overset{iid}{\sim} N(0, \sigma^2)$ $\alpha_{i} \overset{iid}{\sim} N(0, \sigma^2_{\alpha})$
$i \in (1994, 1995,...,2013)$

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